quads to tris leaving some quads
I did the same thing shown in the images above and it looked fine to me but when I went through the Triangulate options, I found that one of the possible settings combinations did produce the results you showed.

Here are both results shown with the settings.  The dialogue box that you see in the images can be accessed by using F6





If you activate Vertex Selection mode and drag out the extra vertex that is seen, what's really happening can be seen.  The model is triangulated properly but the algorithm failed to lay out the geometry properly.  Here is an animation showing this.



You could file a bug report if you like.  https://developer.blender.org/

Personally I'd prefer to locate Ideasman42 and provide him with a link to this page so he can put some thought into this when he's not working on new tools or fixing bigger problems.